The world of modern mathematics abounds with fascinating, unusual ideas ideas and concepts even seasoned mathematicians often wonder about. Mathematical Journeys takes you on a grand tour of the best of modern math its most elegant solutions, most clever discoveries, most mind–bending propositions, and most impressive personalities.
Writing with a light touch while showing the real mathematics, author Peter Schumer introduces you to the history of mathematics, number theory, combinatorics, geometry, graph theory, and "recreational mathematics." Requiring only high school math and a healthy curiosity, Mathematical Journeys helps you explore all those aspects of math that mathematicians themselves find most delightful. You’ll discover brilliant, sometimes quirky and humorous tidbits like how to compute the digits of pi, the Josephus problem, mathematical amusements such as Nim and Wythoff’s game, pizza slicing, and clever twists on rolling dice. For a glimpse of the minds that gave birth to the math, read the profiles of such great thinkers as Paul Erdös and Leonhard Euler.
Each chapter of the book focuses on some interesting piece of mathematics, giving the history and requisite math background, the solution of a problem or two, and some indication of natural generalizations and related areas of study. Whether you’re a math novice curious to learn what your calculus class left out or a math lover ready for the green chicken contest (What’s that? Read the book!), Mathematical Journeys will give you a true taste of what mathematicians themselves find most exciting about math.
1. Let s Get Cooking: A Variety of Mathematical Ingredients.
2. The Green Chicken Contest.
3. The Josephus Problem: Please Choose Me Last.
4. Nim and Wythoff s Game: Or How to Get Others to Pay Your Bar Bill.
5. Mersenne Primes, Perfect Numbers, and Amicable Pairs.
6. The Harmonic Series . . . and Less.
7. Fermat Primes, the Chinese Remainder Theorem, and Lattice Points.
8. Tic–Tac–Toe, Magic Squares, and Latin Squares.
9. Mathematical Variations on Rolling Dice.
10. Pizza Slicing, Map Coloring, Pointillism, and Jack–in–the–Box.
11. Episodes in the Calculation of Pi.
12. A Sextet of Scintillating Problems.
13. Primality Testing Below a Quadrillion.
14. Erdös Number Zero.
15. Choosing Stamps to Mail a Letter, Let Me Count the Ways.
16. Pascal Potpourri.
Appendix: Comments and Solutions to Problems Worth Considering.